Adjustment process of decentralised signal control policies with route choices: a case study with the P0 policy

This study investigates the mathematical properties and network performance of the �0 policy through numerical analysis. We consider a static traffic assignment problem with a �0 policy in a simple signal-controlled network. We then calculate the equilibrium states while changing the demand level from unsaturated to near-saturated to investigate whether uniqueness holds for various traffic demand levels. After investigating the uniqueness through numerical analysis, we examine the stability of the computed equilibrium states using a graphical approach. This approach enables us to assess stability under natural evolutionary dynamics without explicitly specifying the dynamical system. Through these analyses, we demonstrate the occurrence of multiple equilibria with different total travel times at certain moderate traffic demand levels and investigate their stability. We demonstrate that such multiple stable equilibria cause a hysteresis loop, implying that different stable equilibria with different total travel times emerge when traffic demand increases and then decreases.